PHY2061
R. D. Field
Department of Physics
curl_2.doc
Univesity of Florida
Stokes’ Theorem
Stokes’ Theorem:
∫
∫
⋅
=
⋅
×
∇
C
r
d
F
A
d
F
!
!
!
!
!
)
(
Proof (
sketch
):
∫
∑
∑
∫
⋅
×
∇
⇒
⋅
×
∇
=
Γ
=
⋅
=
Γ
→
∞
→
=
=
S
A
N
N
i
i
i
N
i
i
i
i
C
A
d
F
n
F
A
A
A
r
d
F
i
!
!
!
!
!
!
!
)
(
ˆ
)
(
0
1
1
In cartesian (or retangular) coordinates:
z
z
y
y
x
x
∂
∂
+
∂
∂
+
∂
∂
=
ˆ
ˆ
ˆ
!
z
y
x
F
F
F
z
y
x
z
y
x
F
G
∂
∂
∂
∂
∂
∂
=
×
∇
=
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This note was uploaded on 05/31/2011 for the course PHY 2061 taught by Professor Fry during the Spring '08 term at University of Florida.
 Spring '08
 FRY
 Physics

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